Okay, more thoughts about your 2 long & helpful posts above:

I'm not surprised (& don't worry!) that this snake hasn't defecated at all yet. Young rodents are very digestible (smaller bones, less fur)- there isn't much waste leftover for your snake to expel. It's normal for snakes eating young rodents to eat a number of meals before they have to go- it's not a problem, unless he starts looking bloated above his cloaca (aka "vent"), or you feel some hard lumps in that region (snakes occasionally can form urate "stones" that can block them up). So- not to worry.

Reputable snake breeders should be providing feeding records & hatch date- & in some places, are also required to provide a general care sheet. (been there, done that )

Snakes often yawn after eating, to re-set their jaws (so their teeth align properly- their flexible jaws sometimes get a little out of whack). Why your snake yawned when you first got him, I can't say, but if you saw no signs of an RI (bubbles, crackling or whistling sounds, excess saliva) don't worry about it. Good that you thought to check with a vet, just picked the wrong one it seems.

Snakes are very stoic- it's hard enough for a vet to diagnose them, & unless you find a real specialist with experience, many have little knowledge of snake husbandry, even if they're willing to let you pay them for their time. Vets also focus on medical & surgical interventions- they don't have time for discussing every aspect of general care (even if they know), & often, that's what needs to be fixed.

Good that you know to look for "unusual stools"- things like red color (blood) or mucus, etc. Later on, it might be helpful to have a fresh stool sample from this guy analyzed, in case he has intestinal parasites going on, but just work on feeding him for a while now first, & don't worry about it. Eating is "job #1".

Many snakes know instinctively (or from practice) that baby rodents pose no danger to them, so they don't bother constricting. It's fine, not a problem. If he was raised on f/t, that's also why he just ate without fuss. There's nothing wrong with how you offered (though I'd pinch the nose rather than 'braining'- yuck!) & hopefully warmer prey will get a better response from him.

I agree with using smaller hides- something just a little bigger than he is, with only one doorway that's not too big- & low "ceilings" are preferred.

Feeding live is normal for what happens in nature, & often young snakes need to start on live rodents while they're practicing their proper food response- after that, it's best* to switch to f/t or f/k (frozen-thawed or fresh-killed) *because it's more humane, more convenient, & way safer for the snake (sooner or later, snakes get hurt when more mature rodents object to being dinner & bite back). It's fairly unusual for a vet to recommend feeding only live- any exotic vet with much experience has stitched up plenty of snakes injured by their live prey, not to mention that many people keep rodents as pets too. There's also very little nutritional difference for your snake, but live prey can transfer intestinal parasites (worms) to your snake, whereas f/t won't.

There are ways to signal to your snake that you're not incoming prey & avoid nips- for one thing, learn your snake's body language, but also let them know who you are by scent & touch (their best senses). That old story about snakes biting you because you feed them in their home enclosure is just nonsense- spread by those who have learned nothing about communicating with their snakes, or about reading their body language. You're correct about leaving your snake to rest for at least a day or 2 after he eats (once you're handling him, that is).

This seller didn't get back to you because they knew darned well what they did (selling you a snake in poor condition).